Optical matrix elements in tight-binding models with overlap

We investigate the effect of orbital overlap on optical matrix elements in empirical tight-binding models. Empirical tight-binding models assume an orthogonal basis of (atomiclike) states and a diagonal coordinate operator which neglects the intra-atomic part. It is shown that, starting with an atomic basis which is not orthogonal, the orthogonalization process induces intra-atomic matrix elements of the coordinate operator and extends the range of the effective Hamiltonian. We analyze simple tight-binding models and show that nonorthogonality plays an important role in optical matrix elements. In addition, the procedure gives formal justification to the nearest-neighbor spin-orbit interaction introduced by Boykin [Phys. Rev. B 57, 1620 (1998)] in order to describe the Dresselhaus term which is neglected in empirical tight-binding models.